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Matematicheskie Zametki, 2017, Volume 101, Issue 1, Pages 91–100
DOI: https://doi.org/10.4213/mzm11107 (Mi mzm11107) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The One-Dimensional Riemann Problem on an Elliptic Curve

A. A. Matveevaa, V. A. Poberezhnyiab

a National Research University "Higher School of Economics" (HSE), Moscow
b State Scientific Center of the Russian Federation - Institute for Theoretical and Experimental Physics, Moscow
Full-text PDF (433 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm11107
Abstract: A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic.
Keywords: Riemann problem, elliptic curve, logarithmic connection.
Funding agency Grant number
Russian Foundation for Basic Research 16-11-10160
14-01-00547
Ministry of Education and Science of the Russian Federation
Received: 26.06.2016
Revised: 09.08.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 1, Pages 115–122
DOI: https://doi.org/10.1134/S0001434617010114
Bibliographic databases:
Document Type: Article
UDC: 517.925.7
PACS: 02.30.Zz
Language: Russian
Citation: A. A. Matveeva, V. A. Poberezhnyi, “The One-Dimensional Riemann Problem on an Elliptic Curve”, Mat. Zametki, 101:1 (2017), 91–100; Math. Notes, 101:1 (2017), 115–122
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm11107
  • https://doi.org/10.4213/mzm11107
  • https://www.mathnet.ru/eng/mzm/v101/i1/p91
    • This publication is cited in the following 2 articles:
    1. N. Zhan, R. Chen, Ya. You, “Meshfree method based on discrete gas-kinetic scheme to simulate incompressible/compressible flows”, Phys. Fluids, 33:1 (2021), 017112  crossref  isi
    2. A. A. Matveeva, V. A. Poberezhny, “Two-dimensional Riemann problem for rigid representations on an elliptic curve”, J. Geom. Phys., 114 (2017), 384–393  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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